MinT - Information on Result #2245834

Information on Result #2245834

Linear OA(5⁵⁵, 83, F₅, 26) (dual of [83, 28, 27]-code), using 1 times truncation based on linear OA(5⁵⁶, 84, F₅, 27) (dual of [84, 28, 28]-code), using

concatenation of two codes [i] based on
1. linear OA(25¹⁴, 28, F₂₅, 13) (dual of [28, 14, 14]-code), using
  - constructionÂ X applied to RS(12,25) âŠ‚ RS(14,25) [i] based on
    1. linear OA(25¹³, 25, F₂₅, 13) (dual of [25, 12, 14]-code or 25-arc in PG(12,25)), using Reedâ€“Solomon code RS(12,25) [i]
    2. linear OA(25¹¹, 25, F₂₅, 11) (dual of [25, 14, 12]-code or 25-arc in PG(10,25)), using Reedâ€“Solomon code RS(14,25) [i]
    3. linear OA(25¹, 3, F₂₅, 1) (dual of [3, 2, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(25¹, s, F₂₅, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
2. linear OA(5¹, 3, F₅, 1) (dual of [3, 2, 2]-code), using
  - discarding factors / shortening the dual code based on linear OA(5¹, s, F₅, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
    - parity-check code [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(5⁵⁵, 41, F₅, 2, 26) (dual of [(41, 2), 27, 27]-NRT-code)	[i]		OOA Folding